Non-conservative Model Research Articles

Nonconservative kinetic exchange model of opinion dynamics with randomness and bounded confidence

The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values ∈[-1,1]. The characteristics of the unrestricted model, which has one parameter λ representing conviction, undergo drastic changes with the introduction of bounded confidence parametrized by δ. Three distinct regions are identified in the phase diagram in the δ-λ plane and the evidences of a first order phase transition for δ ≥ 0.3 are presented. A neutral state with all opinions equal to zero occurs for λ ≤ λ(c1) ≃ 2/3, independent of δ, while for λ(c(1)) ≤ λ ≤ λ(c(2))(δ), an ordered region is seen to exist where opinions of only one sign prevail. At λ(c(2))(δ), a transition to a disordered state is observed, where individual opinions of both signs coexist and move closer to the extreme values (±1) as λ is increased. For confidence level δ < 0.3, the ordered phase exists for a narrow range of λ only. The line δ = 0 is apparently a line of discontinuity, and this limit is discussed in some detail.

Further analysis of infrared spectrophotometric observations of high area to mass ratio (HAMR) objects in GEO

Optical surveys have identified a class of high area-to-mass ratio (HAMR) objects in the vicinity of the Geostationary Earth Orbit (GEO) ring. The exact origin and nature of these objects are not well known, although their proximity to the GEO belt poses a hazard to active GEO satellites. The prevalent conjecture is that many of these objects may be thermal materials shed from derelict spacecraft in ‘graveyard’ orbits above the GEO ring. Due to their high area-to-mass ratios and unknown attitude dynamics and material characteristics, solar radiation pressure (SRP) perturbs their orbits in ways that makes it difficult to predict their orbital trajectories over periods of time exceeding a week or less. To better understand and track these objects and infer their origins, we have made observations that allow us to determine physical characteristics that will improve the non-conservative force modeling used for orbit determination (OD) and prediction. Information on their temperatures, areas, emissivities, and albedos may be obtained from thermal infrared and visible measurements. Simultaneous observations in the thermal infrared and visible wavelengths may allow disentangling of projected area, albedo, and object emissivity.Further analysis and modeling of observational data on certain of the HAMR objects collected at the AMOS observatory 3.6m AEOS telescope are presented. The thermal-IR spectra of these geosynchronous orbit objects acquired by the Broadband Array Spectrograph System (BASS) span wavelengths 3 to 13μm and constitute a unique data set, providing a means of measuring object fluxes in the infrared and visible wavelengths. These, in turn, allow temperatures and emissivity-area products to be calculated, and in some cases provide information on rotation rates. We compare our observational results with the outputs of simple models, in terms of visible and infrared flux and orbital characteristics. The resulting temperatures and rotation rates are used in SRP acceleration models to demonstrate improvements in OD and prediction performance relative to models which assume default ambient temperature and static attitude dynamics. Additionally, we have the capability and plans to measure material properties with the same instrument in the lab as used at the telescope to facilitate direct comparisons.

Renormalization Group: Applications in Statistical Physics

These notes provide a concise introduction to important applications of the renormalization group (RG) in statistical physics. After reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena, Wilson's momentum shell RG method is presented, and the critical exponents for the scalar Phi^4 model are determined to first order in an eps expansion about d_c = 4. Subsequently, the technically more versatile field-theoretic formulation of the perturbational RG for static critical phenomena is described. It is explained how the emergence of scale invariance connects UV divergences to IR singularities, and the RG equation is employed to compute the critical exponents for the O(n)-symmetric Landau-Ginzburg-Wilson theory. The second part is devoted to field theory representations of non-linear stochastic dynamical systems, and the application of RG tools to critical dynamics. Dynamic critical phenomena in systems near equilibrium are efficiently captured through Langevin equations, and their mapping onto the Janssen-De Dominicis response functional, exemplified by the purely relaxational models with non-conserved (model A) / conserved order parameter (model B). The Langevin description and scaling exponents for isotropic ferromagnets (model J) and for driven diffusive non-equilibrium systems are also discussed. Finally, an outlook is presented to scale-invariant phenomena and non-equilibrium phase transitions in interacting particle systems. It is shown how the stochastic master equation associated with chemical reactions or population dynamics models can be mapped onto imaginary-time, non-Hermitian `quantum' mechanics. In the continuum limit, this Doi-Peliti Hamiltonian is represented through a coherent-state path integral, which allows an RG analysis of diffusion-limited annihilation processes and phase transitions from active to inactive, absorbing states.

The generalized non-conservative model of a 1-planet system revisited

We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular momentum and the spin vectors of the bodies. Thus, we analyze full, spatial model of the planetary system. Both objects are assumed to be deformed due to their own rotations, as well as due to the mutual tidal interactions. The general relativity corrections are considered in terms of the post-Newtonian approximation. Besides the conservative contributions to the perturbing forces, there are also taken into account non-conservative effects, i.e., the dissipation of the mechanical energy. This dissipation is a result of the tidal perturbation on the velocity field in the internal zones with non-zero turbulent viscosity (convective zones). Our main goal is to derive the equations of the orbital motion as well as the equations governing time-evolution of the spin vectors (angular velocities). We derive the Lagrangian equations of the second kind for systems which do not conserve the mechanical energy. Next, the equations of motion are averaged out over all fast angles with respect to time-scales characteristic for conservative perturbations. The final equations of motion are then used to study the dynamics of the non-conservative model over time scales of the order of the age of the star. We analyze the final state of the system as a function of the initial conditions. Equilibria states of the averaged system are finally discussed.

Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects

Nonlinear piezoelectric effects in flexural energy harvesters have recently been demonstrated for drive amplitudes well within the scope of anticipated vibration environments for power generation. In addition to strong softening effects, steady-state oscillations are highly damped as well. Nonlinear fluid damping was previously employed to successfully model drive dependent decreases in frequency response due to the high-velocity oscillations, but this article instead harmonizes with a body of literature concerning weakly excited piezoelectric actuators by modeling nonlinear damping with nonconservative piezoelectric constitutive relations. Thus, material damping is presumed dominant over losses due to fluid-structure interactions. Cantilevers consisted of lead zirconate titanate (PZT)-5A and PZT-5H are studied, and the addition of successively larger proof masses is shown to precipitate nonlinear resonances at much lower base excitation thresholds while increasing the influence of higher-order nonlinearities. Parameter identification results using a multiple scales perturbation solution suggest that empirical trends are primarily due to higher-order elastic and dissipation nonlinearities and that modeling linear electromechanical coupling is sufficient. This article concludes with the guidelines for which utilization of a nonlinear model is preferred.

A new Robust NMPC Scheme and its Application to a Semi-batch Reactor Example

In this paper, a non-conservative robust nonlinear model predictive control scheme that can guarantee satisfaction of the constraints and optimal expected performance under uncertainty is introduced. The proposed control scheme is evaluated by simulations using a well known benchmark problem where the operation of a semi-batch polymerization reactors is optimized under very tight temperature tolerance limits. The simulation results show that the proposed scheme is capable of optimizing the process operation and, at the same time, it ensures robust operation within the whole range of uncertainties.

Global Weak Solutions to One-Dimensional Non-Conservative Viscous Compressible Two-Phase System

In this paper, we deal with global weak solutions of a non-conservative viscous compressible two-phase model in one space dimension. This work extends in some sense the previous work, [Bresch et al., Arch Rat Mech Anal 196:599–629, 2010], which provides the global existence of weak solutions in the multi-dimensional framework with 1 1. Then we prove that any possible vacuum state has to vanish within finite time after which densities are always away from vacuum. This allows to prove that at least one phase corresponding to the global weak solution is a locally in time and space (in a sense to be defined) strong solution after the vacuum states vanish. Our paper may be understood as a non-straightforward generalization to the two-phase flow system of a previous paper [Li et al., Commun Math Phys 281(2):401–444, 2008], which treated the usual compressible barotropic Navier-Stokes equations for mono-fluid with a degenerate viscosity. Various important mathematical difficulties occur when we want to generalize those results to the two-phase flows system since the corresponding model is non-conservative. Far from vacuum, it involves a strong coupling between a nonlinear algebraic system and a degenerate PDE system under constraint linked to fractions. Moreover, fractional densities may vanish if densities or fractions vanish: A difficulty is to find estimates on the densities from estimates on fractional densities using the algebraic system. Original approximate systems have also to be introduced compared to the works on the degenerate barotropic mono-fluid system. Note that even if our result concerns “only” the one-dimensional case, it points out possible global weak solutions (for such a non-conservative system) candidates to approach for instance shock structures and to define an appropriate a priori family of paths in the phase space (in numerical schemes) at the zero dissipation limit.

Criterion of hyperbolicity for non-conservative quasilinear systems admitting a partially convex conservation law

A system of conservation laws admitting an additional convex conservation law can be written as a symmetric t-hyperbolic in the sense of Friedrichs system. However, in mathematical modeling of complex physical phenomena, it is customary to use non-conservative hyperbolic models. We generalize the Godunov–Friedrichs–Lax approach to this new class of models. Copyright © 2011 John Wiley & Sons, Ltd.

Low Energy Impact Indentation of an Epoxy-Carbon Fiber Laminate

The impact event involves the motion of the specimen, the motion of the striker and the local indentation in the contact zone. In order to study the effect of the local indentation, epoxy-carbon fiber laminate specimens supported on a very rigid steel plate, were subjected to low energy impacts in an instrumented falling weight dotted with an instrumented striker with an hemispherical head. The obtained restitution coefficients show that the energy absorption by indentation is not negligible. It has been developed a lumped mass spring model based in the Hertz law which agrees with the experimental contact forces, indenter displacements and restitution coefficient, which give a very good fitting. This non-conservative model allowed assessment of the Young's modulus at these relatively high strain rates.

Large deviation functions in a system of diffusing particles with creation and annihilation

Large deviation functions for an exactly solvable lattice gas model of diffusing particles on a ring, subject to pair annihilation and creation, are obtained analytically using exact free-fermion techniques. Our findings for the large deviation function for the current are compared to recent results of Appert-Rolland et al. [Phys. Rev. E 78, 021122 (2008)] for diffusive systems with conserved particle number. Unlike conservative dynamics, our nonconservative model has no universal finite-size corrections for the cumulants. However, the leading Gaussian part has the same variance as in the conservative case. We also elucidate some properties of the large deviation functions associated with particle creation and annihilation.

Time-resolved infrared spectrophotometric observations of high area to mass ratio (HAMR) objects in GEO

Optical surveys have identified a class of high area-to-mass ratio (HAMR) objects in the vicinity of the Geostationary Earth Orbit (GEO) ring [1]. The exact origin and nature of these objects are not well known, although their proximity to the GEO ring poses a hazard to active GEO satellites. Due to their high area-to-mass ratios, solar radiation pressure perturbs their orbits in ways that makes it difficult to predict their orbital trajectories over periods of time exceeding a week. To better understand these objects and their origins, observations that allow us to derive physical characteristics are required in order to improve the non-conservative force modeling for orbit determination and prediction. Information on their temperatures, areas, emissivities, and albedos may be obtained from thermal infrared, mid-wave infrared (MWIR), and visible measurements. Spectral features may help to identify the composition of the material, and thus possible origins for these objects. We have collected observational data on various HAMR objects from the AMOS observatory 3.6 m AEOS telescope. The thermal-IR spectra of these low-earth orbit objects acquired by the Broadband Array Spectrograph System (BASS) span wavelengths 3–13 μm and constitute a unique data set, providing a means of measuring, as a function of time, object fluxes. These, in turn, allow temperatures and emissivity-area products to be calculated. In some instances we have also collected simultaneous filtered visible photometric data on the observed objects. The multi-wavelength observations of the objects provide possible clues as to the nature of the observed objects. We describe briefly the nature and status of the instrumental programs used to acquire the data, our data of record, our data analysis techniques, and our current results, as well as future plans.

Temperature-controlled molecular dynamics study on velocity-dependent threshold behavior of dynamic nano-friction

Laws of dynamic nano-friction (i.e., continuous wearless friction) were searched for under steady spatial distributions of the local quasi-temperature, by molecular dynamics (MD) simulations. The temperature control of the non-conservative model was carried out by extending the isothermal MD method using the Nosé–Poincaré thermostat. The results suggested that the threshold phenomenon characterizes sliding-velocity dependence of the nano-frictional force between crystal lattices constituting a nano-electromechanical system (NEMS). This phenomenon was turned out to be a universal feature, whether heat transfer to the environment exists or not.

Phase diagram of the ABC model with nonconserving processes

The three species ABC model of driven particles on a ring is generalized to includevacancies and particle-nonconserving processes. The model exhibits phase separation athigh densities. For equal average densities of the three species, it is shown that althoughthe dynamics is local, it obeys detailed balance with respect to a Hamiltonian withlong-range interactions, yielding a nonadditive free energy. The phase diagrams of theconserving and nonconserving models, corresponding to the canonical and grand-canonicalensembles, respectively, are calculated in the thermodynamic limit. Both models exhibit atransition from a homogeneous to a phase-separated state, although the phase diagrams areshown to differ from each other. This conforms with the expected inequivalence ofensembles in equilibrium systems with long-range interactions. These results are based on astability analysis of the homogeneous phase and exact solution of the continuumequations of the models. They are supported by Monte Carlo simulations. This studymay serve as a useful starting point for analyzing the phase diagram for unequaldensities, where detailed balance is not satisfied and thus a Hamiltonian cannot bedefined.

Coupled and uncoupled nonlinear elastic finite element models for monotonically loaded sheathing-to-framing joints in timber based shear walls

Four different elastic models for sheathing-to-framing connections are presented and evaluated on a single connection level and on a shear wall level. Since the models are elastic in their nature they are suitable mainly for cases where the sheathing-to-framing connections are subjected to monotonically increasing displacements. Of the four models one is uncoupled and the others are coupled with respect to the two perpendicular displacement directions in a two-dimensional model. Two of the coupled models are non-conservative, while the third is conservative, indicating a path independency with respect to the work done to reach a defined state of deformation. When the different models are compared it is obvious that the uncoupled model gives strength and stiffness values higher than the others; however it is not obvious which of the models to use in a shear wall analysis, each of the models having its advantages and disadvantages. For the experimental data used as input in the analyses of this study however, a coupled non-conservative model seems the most appropriate.

Structural optimal control for safe Petri nets

This article addresses the problem of forbidden states in both conservative and non-conservative safe Petri net (PN) models. The property of conservativeness is discussed, and its implications are analysed. The construction and formulation of control conditions in the context of safe and non-conservative PN models is investigated, emphasising the problem of control optimality. The fundamental issue studied is that of the equivalence between a forbidden state and its associated constraint. A new fashion of writing control conditions is proposed and used, in conjunction with the place-invariant synthesis method, for the generation of a control solution. The final controlled model obtained is a PN similar in size to the initial model. Finally, the approach is illustrated via a simple example.

A NON-CONSERVATIVE MODEL OF SECOND-ORDER RC SINUSOIDAL OSCILLATORS

In this work we derive a general non-conservative model for any RC sinusoidal oscillator independent of its particular passive topology or the employed active devices. We consider an arbitrary unknown second-order passive RC network terminated at one port by a negative resistor and proceed to impose oscillation start-up and frequency constraints on a derived state-matrix.

Vibrational frequency distribution for nonconservative model of double-walled carbon nanotube

The paper presents the mathematical results for a double-walled carbon nanotube model with nonconservative boundary conditions, given in the form of two Timoshenko beams coupled through a distributed Van Der Waals force. The system is clamped at the left end and subject to a four-parameter family of dynamical boundary conditions at the right end. We also present the four-branch vibrational spectrum of the system. All the results are purely analytical; they will be complemented by numerical simulations in a forthcoming work.

On momentum conservation and thermionic emission cooling

The possibility of increasing the performance of thermionic cooling devices by relaxing lateral momentum conservation is examined. Upper limits for the ballistic emission current are established. It is then shown that for most cases, nonconserved lateral momentum model produces a current that exceeds this upper limit. For the case of heterojunctions with a much heavier effective mass in the barrier and with a low barrier height, however, relaxing lateral momentum may increase the current. These results can be simply understood from the general principle that the current is limited by the location, well or barrier, with the smallest number of conducting channels. They also show that within a thermionic emission framework, relaxing lateral momentum conservation does not increase the upper limit performance in most cases, and when it does, the increase is modest. More generally, however, especially when the connection to the carrier reservoir is poor and performance is well below the upper limit, relaxing lateral momentum conservation could prove beneficial.

Random Walk of Second Class Particles in Product Shock Measures

We consider shock measures in a class of conserving stochastic particle systems on Z. These shock measures have a product structure with a step-like density profile and include a second class particle at the shock position. We show for the asymmetric simple exclusion process, for the exponential bricklayers' process, and for a generalized zero range process, that under certain conditions these shocks, and therefore the second class particles, perform a simple random walk. Some previous results, including random walks of product shock measures and stationary shock measures seen from a second class particle, are direct consequences of our more general theorem. Multiple shocks can also be handled easily in this framework. Similar shock structure is also found in a nonconserving model, the branching coalescing random walk, where the role of the second class particle is played by the rightmost (or leftmost) particle.

GSFC DORIS contribution to ITRF2008

The NASA GSFC DORIS analysis center has provided weekly DORIS solutions from November 1992 to January 2009 (839 SINEX files) of station positions and Earth Orientation Parameters for inclusion in the DORIS contribution to ITRF2008. The NASA GSFC GEODYN orbit determination software was used to process the orbits and produce the normal equations. The weekly SINEX gscwd10 submissions included DORIS data from Envisat, TOPEX/Poseidon, SPOT-2, SPOT-3, SPOT-4, SPOT-5. The orbits were mostly seven days in length (except for weeks with data gaps or maneuvers). The processing used the GRACE-derived EIGEN-GL04S1 gravity model, updated modeling for time-variable gravity, the GOT4.7 ocean tide model and tuned satellite-specific macromodels for SPOT-2, SPOT-3, SPOT-4, SPOT-5 and TOPEX/Poseidon. The University College London (UCL) radiation pressure model for Envisat improves nonconservative force modeling for this satellite, reducing the median residual empirical daily along-track accelerations from 3.75 × 10 −9 m/s 2 with the a priori macromodel to 0.99 × 10 −9 m/s 2 with the UCL model. For the SPOT and Envisat DORIS satellite orbits from 2003 to 2008, we obtain average RMS overlaps of 0.8–0.9 cm in the radial direction, 2.1–3.4 cm cross-track, and 1.7–2.3 cm along-track. The RMS orbit differences between Envisat DORIS-only and SLR & DORIS orbits are 1.1 cm radially, 6.4 cm along-track and 3.7 cm cross-track and are characterized by systematic along-track mean offsets due to the Envisat DORIS system time bias of ±5–10 μs. We obtain a good agreement between the geometrically-determined geocenter parameters and geocenter parameters determined dynamically from analysis of the degree one terms of the geopotential. The intrinsic RMS weekly position repeatability with respect to the IDS-3 combination ranges from 2.5 to 3.0 cm in 1993–1994 to 1.5 cm in 2007–2008.